Abstract

A multiple-scattering Monte Carlo model that can produce near-photographic quality images is developed and used to simulate several dramatic halo displays. The model atmosphere contains an absorbing ozone layer plus two clear, molecular air layers with Rayleigh scattering surrounding a cloud layer and an atmospheric boundary layer with aerosol particles subject to Lorentz–Mie scattering. Halos are produced by right hexagonal or pyramidal crystals that reflect and refract according to geometric optics without diffraction, although “junk” crystals with a pronounced forward-scattering peak but no halo peaks may be included to simulate typical, faint halos. Model parameters include ozone height and content, surface and cloud pressure, cloud optical thickness, crystal shapes, orientations and abundances, atmospheric turbidity, aerosol radius, and albedo. Beams for each wavelength are sorted into small bins as halo beams if they have been scattered once only by a single crystal and otherwise as sky beams, which are smoothed and combined with the halo beams to produce images. Multiple scattering generally vitiates halos, but extremely rare halos, such as Kern’s arc, can be produced if a significant fraction of crystals in optically thick clouds have identical shapes and are highly oriented. Albedo is a model by-product with potential value in climate studies.

A reviewer pointed out that these unusual halo arcs may be identified with arcs photographed in a searchlight display by M. Riikonen, “Circular subanthelic halo from 3-5-6-7-(2)-3 raypath,” http://www.ursa.fi/blogit/ice_crystal_halos/index.php?m=20081216 (2008).

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A reviewer pointed out that these unusual halo arcs may be identified with arcs photographed in a searchlight display by M. Riikonen, “Circular subanthelic halo from 3-5-6-7-(2)-3 raypath,” http://www.ursa.fi/blogit/ice_crystal_halos/index.php?m=20081216 (2008).

Graph of relative dot density (radiance) versus zenith angle in the vertical plane of the Sun for the image of Fig. 3 for τcld=0.5: black curve, light only scattered by one crystal; gray (red online) curve, other scattered light.

Fish-eye image of the simulated display of odd-radius halos at 31,000 feet over British Columbia generated by randomly oriented crystals composed of 50% pencils and 50% pyramidal crystals with dimensions given in the text for ϕSUN=40°, β=1.0, psfc=700hPa and pcld=300hPa, and τcld=0.05.

Graph of relative dot density (radiance) versus zenith angle in the vertical plane for the simulation of Fig. 9. The black curve gives light only scattered by one crystal, and the gray (red online) curve gives the other scattered light.